arXiv:2605.23712cs.CEcs.LG2026-05

用语言模型框架从稀疏数据重建流场,无需网格划分。

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: a Language Model Approach

论文配图:Operator Learning for Reconstructing Flow Fields from Sparse Measurements: a Language Model Approach
图 1 · 摘自论文原文
  • 将流场重构转为序列到序列任务,利用上下文推断未知点。
  • 在不足10%数据条件下仍保持高精度,三維湍流流场也有效。
  • 适合需要高效、无网格流场重建的科研与工程场景。

从稀疏测量中重构流场是流体力学中的基础问题,对建模、控制和设计具有广泛影响。本文提出一种新型算子学习框架,借鉴语言模型架构,在无网格条件下实现流场重建。将流场重构转化为序列到序列学习任务:稀疏测量作为上下文,未观测位置作为查询。模型能从稀疏输入中学习空间相关性与长程依赖,重建完整流场。在四个基准数据集上评估:(1) 二维涡街模拟,(2) 美国本土日均气温数据,(3) 基于耗散粒子动力学的三维血流模拟,(4) 基于粒子追踪测速获得的三维湍流射流测量。所有情况下,方法在极不完整数据(<10%观测)下仍具竞争力的重建精度,并实现高效性能。结果表明,语言模型可作为科学数据重建的鲁棒且可扩展工具,为科学与工程领域基础模型的发展提供新方向。

原文摘要 · Abstract (English)

Reconstructing flow fields from sparse measurements is a fundamental problem in fluid mechanics with broad implications for modeling, control, and design. In this work, we propose a novel operator learning framework that leverages the architecture of language models to perform flow reconstruction in a mesh-free manner. We reformulate flow field reconstruction as a sequence-to-sequence learning task, where sparse measurements are treated as context and unobserved locations as queries. Our model learns to reconstruct the full flow field from sparse inputs, effectively capturing spatial correlations and long-range dependencies. We evaluate the proposed approach on four benchmark datasets: (1) two-dimensional vortex street simulations, (2) daily average temperature data across the contiguous United States, (3) three-dimensional blood flow simulations based on dissipative particle dynamics, and (4) three-dimensional turbulent jet flow measurements obtained via particle tracking velocimetry. Across all cases, our method demonstrates competitive reconstruction accuracy, even with highly incomplete data (less than 10\% observed), and achieves efficient performance. The results highlight the potential of language models as robust and scalable tools for scientific data reconstruction, and suggest a promising direction toward the development of foundation models for scientific and engineering applications.

流场重建语言模型算子学习无网格

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